If 2^(a)=root(9)(2^(4)), what is the value of a ? ◻

Rewrite Equation: Understand the given equation and rewrite it in a more familiar form. The ninth root of 2^(4) can be written as (2^(4))^(1/9). So, the equation becomes 2^(a) = (2^(4))^(1/9).Apply Power Rule: Apply the power rule of exponents which states that (x^(m))^n = x^(m*n). So, (2^(4))^(1/9) becomes 2^(4*(1/9)).Simplify Exponents: Multiply the exponents to simplify the right side of the equation. 4*(1/9) = 4/9. So, 2^(a) = 2^(4/9).Solve for a: Since the bases are the same and the equation is an equality, the exponents must be equal. Therefore, a = 4/9.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
2^(a)=root(9)(2^(4)), what is the value of
a ?

◻

If $2^{a}=\sqrt[9]{2^{4}}$ , what is the value of $a$ ? $\newline$ ◻

View step-by-step help

Home

Math Problems

Algebra 2

Csc, sec, and cot of special angles

Full solution

Q. If

2^{a}=\sqrt[9]{2^{4}}

, what is the value of

a

\newline

◻

Rewrite Equation: Understand the given equation and rewrite it in a more familiar form. $\newline$ The ninth root of $2^{4}$ can be written as $(2^{4})^{\frac{1}{9}}$ . $\newline$ So, the equation becomes $2^{a} = (2^{4})^{\frac{1}{9}}$ .
Apply Power Rule: Apply the power rule of exponents which states that $(x^{m})^{n} = x^{m*n}$ . $\newline$ So, $(2^{4})^{\frac{1}{9}}$ becomes $2^{4*\frac{1}{9}}$ .
Simplify Exponents: Multiply the exponents to simplify the right side of the equation. $\newline$ $4\times\left(\frac{1}{9}\right) = \frac{4}{9}$ . $\newline$ So, $2^{a} = 2^{\frac{4}{9}}$ .
Solve for $a$ : Since the bases are the same and the equation is an equality, the exponents must be equal. $\newline$ Therefore, $a = \frac{4}{9}$ .