( x^5 y^-3 / 5x^9) ^-2
i cant figure this out ;( i need help
The exponent of -2 must be multiplied into each exponent... So the numerator would be x^-10y^6
Once you have multiplied the -2 into the denominator exponents, then when the bases are the same combine the exponents : )
would the answer be 10^28 y^6 / 25
(x^5y^-3/5x^9)^-2.
(x^-4y^-3/5)^-2,
x^8y^6/5^-2,
x^8y^6(5^2) = 25x^8y^6.
Sure, I can help you with that! Let's break it down step by step.
The expression you have is: ( x^5 y^-3 / 5x^9) ^-2
Step 1: Start by simplifying the expression inside the parentheses.
The numerator, x^5, stays the same.
The denominator, 5x^9, can be rewritten as (5 * x^9), so we have: ( x^5 y^-3 / (5 * x^9))
Step 2: To simplify further, divide the x^5 in the numerator by the x^9 in the denominator.
When you divide variables with the same base, you subtract the exponents: x^(5 - 9) = x^(-4).
So, the expression now becomes: ( y^-3 / (5 * x^(-4)) )
Step 3: Next, let's deal with the y^-3.
Negative exponents indicate reciprocal. So, y^-3 can be written as 1/y^3.
The expression becomes: ( 1/y^3 / (5 * x^(-4)) )
Step 4: To simplify further, multiply the numerator and denominator by the reciprocal of (5 * x^(-4)).
The reciprocal of (5 * x^(-4)) is (1 / (5 * x^(-4))).
Multiplying the numerator and denominator by (1 / (5 * x^(-4))) cancels out the fraction in the denominator. We are left with:
( 1 * (1 / (5 * x^(-4))) ) / y^3
Step 5: Simplify the expression further.
When you divide by a fraction, you multiply by its reciprocal. So, dividing by (1 / (5 * x^(-4))) is the same as multiplying by (5 * x^(-4)).
The expression becomes: (1 * (5 * x^(-4))) / y^3
Step 6: Multiply the coefficients (5 * 1) and combine the x-terms.
We can rewrite 5 as 5 * 1, so the expression becomes: 5x^(-4) / y^3
Step 7: Finally, let's deal with the negative exponent.
Negative exponents can be rewritten as fractions with positive exponents: x^(-4) = 1 / x^4.
The expression is now: 5 / (x^4 * y^3)
So, the final simplified expression is: 5 / (x^4 * y^3).