Rewrite 8 as 2^3: We are given the equation 8^(x/3) = 2. We know that 8 can be expressed as 2^3. Let's rewrite 8 in terms of 2.Apply power rule: Replace 8 with 2^3 in the equation. (2^3)^(x/3) = 2 Now, apply the power of a power rule, which states that (a^b)^c = a^(b*c).Simplify left side: Simplify the left side of the equation using the power of a power rule. 2^(3*(x/3)) = 2 2^(x) = 2Set exponents equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. x = 1

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$8^{\frac{x}{3}} = 2$

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Math Problems

Grade 6

Find the missing exponent or base

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8^{\frac{x}{3}} = 2

Rewrite $8$ as $2^3$ : We are given the equation $8^{(x/3)} = 2$ . We know that $8$ can be expressed as $2^3$ . Let's rewrite $8$ in terms of $2$ .
Apply power rule: Replace $8$ with $2^3$ in the equation. $\newline$ $(2^3)^{(x/3)} = 2$ $\newline$ Now, apply the power of a power rule, which states that $(a^b)^c = a^{(b*c)}$ .
Simplify left side: Simplify the left side of the equation using the power of a power rule. $\newline$ $2^{3*(x/3)} = 2$ $\newline$ $2^{x} = 2$
Set exponents equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. $x = 1$