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. $\newline$ $(4d^6)^3$

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

(4d^6)^3

Apply power rule: Apply the power of a power rule to the expression $(4d^6)^3$ . The power of a power rule states that when raising a power to another power, you multiply the exponents. For the coefficient $4$ , which is raised to the power of $1$ implicitly, we will also apply the same rule. $(4d^6)^3 = 4^3 \times (d^6)^3$
Calculate $4^3$ : Calculate $4^3$ . $\newline$ $4^3 = 4 \times 4 \times 4 = 64$
Calculate $(d^6)^3$ : Calculate $(d^6)^3$ . $(d^6)^3 = d^{(6 \times 3)} = d^{18}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(4d^6)^3 = 4^3 \times (d^6)^3 = 64 \times d^{18}$
Write final expression: Write the final simplified expression. $\newline$ The expression $(4d^6)^3$ simplifies to $64d^{18}$ .

More problems from Powers of a power: variable bases

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 2 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 2 months ago

Question

x^2 = 4

Posted 1 month ago

Question

x^2 = 9

Posted 3 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 3 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 3 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 3 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 4 days 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 1 month 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 1 month ago