I need help simplifing multiple exponents with integers. I.E (-2y^-3)^-3
To simplify an expression with multiple exponents, you can follow these steps:
Step 1: Start by simplifying the exponents within the parentheses using the power of a power rule.
In this case, the exponent of -3 will be applied to both -2 and y^-3 inside the parentheses.
(-2y^-3)^-3 = (-2^-3)(y^-3 * -3)
Step 2: Simplify the negative exponents using the negative exponent rule.
The negative exponent rule states that any term with a negative exponent can be moved to the opposite side of the fraction bar and made positive.
(-2^-3)(y^-3 * -3) = (-1/2^3)(1/y^3 * -3)
Step 3: Evaluate the exponential expressions.
In this case, -2^3 = -8 and (-1/2^3) = -1/8. Additionally, y^-3 * -3 simplifies to (-3/y^3).
(-1/2^3)(1/y^3 * -3) = (-1/8)(-3/y^3)
Step 4: Simplify further if possible.
Multiply the coefficients (-1/8)(-3) = 3/8 and combine the variables as necessary.
(-1/8)(-3/y^3) = 3/8y^3
Therefore, the simplified expression is 3/8y^3.