Numbers and Decimals

Basic Arithmetic

Number Line and Comparing Numbers

Place Value and Rounding Numbers

Basic Arithmetic and Inverse Operations

BIDMAS – Order of Operations

Commutative Property and Associative Property

Distributive Property

Column Addition and Column Subtraction

Long Multiplication

Factors and Multiples

Divisibility and Divisibility Rules

Prime Numbers and Prime Factorization

How to Find HCF and LCM

Powers and Roots

Powers and Indices

Basics of Square Roots

Multiplying and Dividing Square Roots

The nth Root and Fractional Indices

Laws of Indices (Same Base, Same Indices)

Negative Exponents and Power of a Power

Decimals

Decimals and Fractions

Comparing and Rounding Decimals

1 of 2

Previous Lesson

{results_count} Math videos for {phrase}

Displaying {results_count} results of {results_count_total}

Generic filters

Exact matches only

Search in title

Search in content

Search in excerpt

Filter by Lesson Categories

Negative Exponents and Power of a Power

Numbers and Decimals Negative Exponents and Power of a Power

Courses Overview

🎬 Video Tutorial

(0:10) How to Simplify Negative Exponents: A negative exponent means taking the reciprocal of the base with its positive exponent. For example: $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$
(1:03) Applying Negative Indices Rule on Fractions: Flip the fraction and use the positive index. For example: $\left(\frac{2}{3}\right)^{-2} = \left(\frac{3}{2}\right)^2 = \frac{9}{4}$
(1:34) What is Power of a Power Rule?: When raising a power to a power, multiply the indices. For example: $(2^3)^5 = 2^{3 \times 5} = 2^{15}$

📂 Revision Cards

Indices rules showing negative exponents and power of a power with examples. — 1) Negative Exponents & Power of a Power

Negative indices rules shown with examples. — 2) Applying Negative Indices Rule on Fractions

3) Power of a Power Rules

4) Power of a Power Rules

🍪 Quiz Time - Practice Now!

0%

Laws of Indices (Negative Indices and Power of a Power)

1 / 6

Q: What is $(2^3)^5$?

$2^{13}$

$2^8$

$2^{15}$

$2^{5}$

Feedback: Not quite! When raising a number to a power and then raising it again, multiply the exponents. The formula is $(a^m)^n = a^{m \times n}$. So, $(2^3)^5 = 2^{3 \times 5} = 2^{15}$.

Feedback: Well done! When raising a number to a power and then raising it again, multiply the exponents. The formula is $(a^m)^n = a^{m \times n}$. So, $(2^3)^5 = 2^{3 \times 5} = 2^{15}$.

2 / 6

Q: What is $4^{-1}$?

$\frac{1}{4}$

-4

4

$-\frac{1}{4}$

Feedback: Not quite! A negative exponent means you take the reciprocal of the base and change the exponent to positive. The formula here is $a^{-1} = \frac{1}{a}$. So, $4^{-1} = \frac{1}{4}$.

Feedback: Well done! A negative exponent means you take the reciprocal of the base and change the exponent to positive. The formula here is $a^{-1} = \frac{1}{a}$. So, $4^{-1} = \frac{1}{4}$.

3 / 6

Q: What is $2^{-3}$?

$\frac{1}{6}$

-6

$\frac{1}{8}$

-8

Feedback: Not quite! A negative exponent means you take the reciprocal of the base and change the exponent to positive. The formula is $a^{-n} = \frac{1}{a^n}$. So, $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$.

Feedback: Well done! A negative exponent means you take the reciprocal of the base and change the exponent to positive. The formula is $a^{-n} = \frac{1}{a^n}$. So, $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$.

4 / 6

Q: What is $(-5)^{-3}$?

$\frac{1}{-125}$

125

$\frac{1}{125}$

-125

Feedback: Not quite! A negative exponent means you flip the base and make the exponent positive. The formula is $a^{-n} = \frac{1}{a^n}$. So, $(-5)^{-3} = \frac{1}{(-5)^3} = \frac{1}{-125}$.

Feedback: Well done! A negative exponent means you flip the base and make the exponent positive. The formula is $a^{-n} = \frac{1}{a^n}$. So, $(-5)^{-3} = \frac{1}{(-5)^3} = \frac{1}{-125}$.

5 / 6

Q: What is $(5^{-2})^2$?

$\frac{1}{5^2}$

$\frac{1}{5^4}$

$5^4$

$5^{-4}$

Feedback: Not quite! When raising a number with a negative exponent to another power, you multiply the exponents. The formula is $(a^m)^n = a^{m \times n}$. So, $(5^{-2})^2 = 5^{-2 \times 2} = 5^{-4}$.

Feedback: Well done! When raising a number with a negative exponent to another power, you multiply the exponents. The formula is $(a^m)^n = a^{m \times n}$. So, $(5^{-2})^2 = 5^{-2 \times 2} = 5^{-4}$.

6 / 6

Q: What is $(\frac{1}{2})^{-3}$?

$2^3$

$2^{-3}$

$\frac{1}{8}$

8

Feedback: Not quite! A negative exponent means you flip the base and make the exponent positive. The formula is $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$. So, $(\frac{1}{2})^{-3} = 2^3 = 8$.

Feedback: Well done! A negative exponent means you flip the base and make the exponent positive. The formula is $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$. So, $(\frac{1}{2})^{-3} = 2^3 = 8$.

Your score is

The average score is 72%

0%

🎩 AI Math Solver (ChatCat)

Need math help? Chat with our AI Math Solver at the bottom right!

Previous Lesson

0 0 votes

Article Rating

Label

Name*

Email

Label

Name*

Email

0 Comments

Newest

Oldest Most Voted

Inline Feedbacks

View all comments

Leave a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Comment *

Name

Email

Website

Save my name, email, and website in this browser for the next time I comment.

ChatCat

Log In

Username or Email Address

Password

Remember Me

Join Now | Lost Password?

Login

Accessing this course requires a login. Please enter your credentials below!

Username or Email Address

Password

Remember Me

Lost Your Password?

Register

Don't have an account? Register one!

Register an Account