Question

Simplify the exponential expression. Assume that the variable represents a nonzero real number.
left parenthesis y Superscript 8 right parenthesis Superscript negative 6
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Part 1
left parenthesis y Superscript 8 right parenthesis Superscript negative 6equals
  
enter your response here ​(Use positive exponents​ only.)

Answer 1

To simplify the expression \((y^8)^{-6}\), we can use the properties of exponents. Specifically, we can apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\).

So, we calculate:
\[
(y^8)^{-6} = y^{8 \cdot (-6)} = y^{-48}
\]

Next, to express the result using only positive exponents, we use the property that \(a^{-n} = \frac{1}{a^n}\):
\[
y^{-48} = \frac{1}{y^{48}}
\]

Thus, the simplified expression is:
\[
\frac{1}{y^{48}}
\]