Fully simplify
(z^-5\cdotz^9)^8
To fully simplify (z^-5 * z^9)^8, we need to first simplify the expression inside the parentheses and then apply the exponent outside.
Inside the parentheses, we can multiply the two terms with the same base, z. When we multiply terms with the same base, we add their exponents.
So, (z^-5 * z^9) becomes z^(-5 + 9) which becomes z^4.
Now, the expression becomes (z^4)^8. When we raise a term with an exponent to another exponent, we multiply the exponents.
So, (z^4)^8 becomes z^(4 * 8) which becomes z^32.
Therefore, the fully simplified expression is z^32.
To fully simplify the expression \((z^{-5} \cdot z^9)^8\), we can use the rules of exponents.
First, let's simplify the expression inside the parentheses by multiplying the exponents together:
\(z^{-5} \cdot z^9 = z^{(-5 + 9)} = z^4\)
Next, we raise \(z^4\) to the 8th power by multiplying the exponent by 8:
\((z^4)^8 = z^{(4 \cdot 8)} = z^{32}\)
So, \((z^{-5} \cdot z^9)^8\) simplifies to \(z^{32}\).
To fully simplify the expression (z^-5 * z^9)^8, it is important to understand the rules of exponents.
The rule of exponents states that when you multiply two terms with the same base, you need to add their exponents. In this case, the base is "z," and we have z^-5 and z^9.
So, let's simplify the expression step by step:
First, let's simplify the term within the parentheses: (z^-5 * z^9)
To multiply these terms, we add their exponents: z^-5 * z^9 = z^(-5 + 9) = z^4
Now, we rewrite the expression with the simplified term: (z^4)^8
To raise a power to another power, we multiply the exponents. In this case, we have z^4 raised to the power of 8.
(z^4)^8 = z^(4 * 8) = z^32
Therefore, the fully simplified expression is z^32.