Fully simplify
(z^-3\cdotz^-7)^-4
To fully simplify (z^-3 · z^-7)^-4, we need to apply the rules of exponents.
First, we can multiply the exponents inside the parentheses by -4:
(z^-3 · z^-7)^-4 = z^(-3 * -4) · z^(-7 * -4)
Simplifying the exponents further:
= z^12 · z^28
Now, we can combine these two exponents by adding them together:
= z^(12 + 28)
= z^40
Therefore, the fully simplified expression is z^40.
To fully simplify the expression (z^-3 * z^-7)^-4, we can use the properties of exponents.
First, let's simplify the expression inside the parentheses: z^-3 * z^-7.
When multiplying expressions with the same base, we add the exponents. So, z^-3 * z^-7 is equal to z^(-3 + -7) = z^-10.
Now, let's simplify the expression with the exponent -4.
When raising a number with an exponent to another exponent, we multiply the exponents. So, (z^-10)^-4 is equal to z^((-10) * (-4)) = z^40.
Therefore, the fully simplified expression is z^40.
To fully simplify the expression, let's start by simplifying the exponents.
First, we can apply the power of a power rule, which states that to raise an exponent to a power, we multiply the exponents together. In this case, we have:
(z^(-3) ⋅ z^(-7))^(-4)
Using the power of a power rule, we can multiply the exponents:
z^((-3) ⋅ (-4)) ⋅ z^((-7) ⋅ (-4))
This simplifies to:
z^12 ⋅ z^28
Next, we need to apply the product of powers rule, which states that when multiplying powers with the same base, we can add the exponents together. In this case, we have:
z^12 ⋅ z^28
Using the product of powers rule, we can add the exponents:
z^(12 + 28)
This simplifies to:
z^40
So, the fully simplified expression is z^40.