QuestionAugust 24, 2025

If (6^3)^x=6^15 , what is the value of x? square

If (6^3)^x=6^15 , what is the value of x? square
If (6^3)^x=6^15 , what is the value of x?
square

Solution
4.3(395 votes)

Answer

5 Explanation 1. Simplify the left side Use the power of a power rule: (a^m)^n = a^{m \cdot n}. So, (6^3)^x = 6^{3x}. 2. Set exponents equal Since the bases are the same, set the exponents equal: 3x = 15. 3. Solve for x Divide both sides by 3: x = \frac{15}{3}.

Explanation

1. Simplify the left side<br /> Use the power of a power rule: $(a^m)^n = a^{m \cdot n}$. So, $(6^3)^x = 6^{3x}$.<br />2. Set exponents equal<br /> Since the bases are the same, set the exponents equal: $3x = 15$.<br />3. Solve for x<br /> Divide both sides by 3: $x = \frac{15}{3}$.
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