Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Express your answer using a single exponent. $\newline$ $(7u^3)^2$

View step-by-step help

View step-by-step help

Powers of a power: variable bases

Full solution

Q. Simplify. Express your answer using a single exponent.

\newline

(7u^3)^2

Apply Power Rule: Apply the power to a power rule. $\newline$ When raising a power to another power, we multiply the exponents. For the expression $(7u^3)^2$ , we apply the exponent of $2$ to both the base $7$ and the exponent of $u^3$ . $\newline$ $(7u^3)^2 = 7^2 \times (u^3)^2$
Calculate $7^2$ : Calculate $7^2$ . $\newline$ $7^2$ is $7$ multiplied by itself. $\newline$ $7^2 = 7 \times 7 = 49$
Calculate $(u^3)^2$ : Calculate $(u^3)^2$ . When raising a power to another power, we multiply the exponents. The exponent for $u$ is $3$ , and we are raising it to the power of $2$ . $(u^3)^2 = u^{(3 \times 2)} = u^6$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ We have found that $7^2 = 49$ and $(u^3)^2 = u^6$ . Now we combine these to express the simplified form of the original expression. $\newline$ $(7u^3)^2 = 49 \times u^6 = 49u^6$

More problems from Powers of a power: variable bases

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 9 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 9 months ago

Question

x^2 = 4

Posted 7 months ago

Question

x^2 = 9

Posted 10 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 10 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 10 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 10 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 6 months ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 8 months ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant