Question

Simplify the exponential expression. Assume that the variable represents a nonzero real number.
left parenthesis y Superscript 6 right parenthesis Superscript negative 7
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Part 1
left parenthesis y Superscript 6 right parenthesis Superscript negative 7equals
  
enter your response here ​(Use positive exponents​ only.)

Answer 1

To simplify the expression \((y^6)^{-7}\), we apply the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

So, we multiply the exponents:

\[
(y^6)^{-7} = y^{6 \cdot (-7)} = y^{-42}
\]

Now, since we want to express this with positive exponents only, we use the property that \(a^{-n} = \frac{1}{a^n}\):

\[
y^{-42} = \frac{1}{y^{42}}
\]

Thus, the simplified expression is:

\[
\frac{1}{y^{42}}
\]