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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^(2))^((6)/(5))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x2)65=xa \left(x^{2}\right)^{\frac{6}{5}}=x^{a} \newlineAnswer:

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Full solution

Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x2)65=xa \left(x^{2}\right)^{\frac{6}{5}}=x^{a} \newlineAnswer:
  1. Apply Power Rule: Apply the power of a power rule to simplify the left-hand side of the equation.\newlineThe power of a power rule states that (xm)n=xm∗n(x^m)^n = x^{m*n}. In this case, m=2m = 2 and n=65n = \frac{6}{5}.\newlineSo, (x2)(65)=x2∗(65)(x^{2})^{(\frac{6}{5})} = x^{2*(\frac{6}{5})}.
  2. Find Exponent: Perform the multiplication to find the exponent. 2×(65)=1252 \times (\frac{6}{5}) = \frac{12}{5}. So, x2×(65)=x125x^{2\times(\frac{6}{5})} = x^{\frac{12}{5}}.
  3. Equate Exponents: Since the left-hand side of the equation is now simplified to x125x^{\frac{12}{5}}, we can equate the exponents on both sides of the equation to find the value of aa. Therefore, a=125a = \frac{12}{5}.

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