Fully simplify
(y^8\cdoty^8)^5/(y^4\cdoty^3)^2
To simplify the expression, we can use the properties of exponents to combine the terms with the same bases.
First, let's simplify the numerator:
(y^8 * y^8)^5 = y^(8*5) * y^(8*5) = y^40 * y^40 = y^(40+40) = y^80
Now, let's simplify the denominator:
(y^4 * y^3)^2 = y^(4*2) * y^(3*2) = y^8 * y^6 = y^(8+6) = y^14
So, the simplified expression is:
(y^8 * y^8)^5 / (y^4 * y^3)^2 = y^80 / y^14
To divide with the same base, we subtract the exponents:
y^80 / y^14 = y^(80-14) = y^66
Therefore, the fully simplified expression is y^66.
To simplify the expression (y^8 * y^8)^5 / (y^4 * y^3)^2, let's break it down step by step:
First, let's simplify the exponents within the parentheses on the numerator:
(y^8 * y^8)^5 = y^(8*5) = y^40
Next, let's simplify the exponents within the parentheses on the denominator:
(y^4 * y^3)^2 = (y^(4+3))^2 = (y^7)^2 = y^(7*2) = y^14
Now, we substitute these simplified expressions back into the original expression:
(y^8 * y^8)^5 / (y^4 * y^3)^2 = y^40 / y^14
To simplify further, we subtract the exponents:
y^40 / y^14 = y^(40-14) = y^26
Therefore, the fully simplified expression is y^26.
To fully simplify the expression:
First, we can simplify each parentheses separately.
For the numerator:
(y^8 * y^8)^5 = y^(8 * 5 + 8 * 5) = y^80
For the denominator:
(y^4 * y^3)^2 = y^(4 * 2 + 3 * 2) = y^14
Now, the expression becomes:
y^80 / y^14
Next, we will use the rule of exponentiation which states that dividing two numbers with the same base results in subtracting their exponents.
Applying this rule, we subtract the exponents:
y^(80 - 14) = y^66
Therefore, the fully simplified expression is y^66.