In the following equation, what is the value of d? (3^d)^10 = 3^20 d = ____

Simplify Power Rule: Simplify the left side of the equation using the power of a power rule, (a^m)^n = a^(m*n). Calculation: (3^d)^10 = 3^(d*10)Set Equal: Set the simplified equation equal to the right side of the original equation. 3^(d*10) = 3^20Set Exponents Equal: Since the bases are the same (3), set the exponents equal to each other. d*10 = 20Solve for d: Solve for d by dividing both sides by 10. d = 20 / 10 d = 2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In the following equation, what is the value of $d$ ? $\newline$ $(3^d)^{10} = 3^{20}$ $\newline$ d = ____

View step-by-step help

Home

Math Problems

Grade 7

Evaluate nonlinear expressions

Full solution

Q. In the following equation, what is the value of

d

\newline

(3^d)^{10} = 3^{20}

\newline

d = ____

Simplify Power Rule: Simplify the left side of the equation using the power of a power rule, $(a^m)^n = a^{m*n}$ . $\newline$ Calculation: $(3^d)^{10} = 3^{d*10}$
Set Equal: Set the simplified equation equal to the right side of the original equation. $\newline$ $3^{d\cdot 10} = 3^{20}$
Set Exponents Equal: Since the bases are the same $3$ , set the exponents equal to each other. $d\cdot 10 = 20$
Solve for d: Solve for d by dividing both sides by $10$ . $d = \frac{20}{10}$ $d = 2$