Simplify (z^-2\cdotz^7)^6
To simplify the expression (z^-2\cdotz^7)^6, we can use the rule that states when raising a power to another power, we need to multiply the exponents.
First, let's simplify the expression inside the parentheses:
z^-2\cdotz^7 can be rewritten as z^(-2+7) = z^5.
So now we have (z^5)^6.
To simplify this further, we multiply the exponents:
(z^5)^6 = z^(5*6) = z^30.
Therefore, the simplified expression is z^30.
Simplify (y^8\cdoty^8)^5
To simplify the expression (y^8\cdoty^8)^5, we can use the rule that states when multiplying two powers with the same base, we add the exponents.
First, let's simplify the expression inside the parentheses:
y^8\cdoty^8 can be rewritten as y^(8+8) = y^16.
So now we have (y^16)^5.
To simplify this further, we multiply the exponent by the power:
(y^16)^5 = y^(16*5) = y^80.
Therefore, the simplified expression is y^80.
To simplify the expression (z^-2 * z^7)^6, we can use the properties of exponents.
First, we can multiply the exponents inside the parentheses:
z^-2 * z^7 = z^(7-2) = z^5
Now we have (z^5)^6. To simplify, we multiply the exponents:
(z^5)^6 = z^(5*6) = z^30
Therefore, (z^-2 * z^7)^6 simplifies to z^30.