How do you solve this equations?
(xy^-3)^-5
(3x^4)(4x^12)
ab^-6
______
c^0d^-4
x^3y^0(z^-4)
Can you please show it step by step?
Thanks.
Sure! Let's solve each equation step by step:
1. (xy^-3)^-5:
To solve this equation, we will use the rule of exponents which states that when we have a negative exponent, we can rewrite it as the reciprocal of the positive exponent. Let's break it down step by step:
(xy^-3)^-5 = x^-5 * (y^-3)^-5
= x^-5 * y^15
= 1 / x^5 * y^15
2. (3x^4)(4x^12):
To solve this equation, we multiply the coefficients together and then multiply the variables together by adding their exponents. Here's how it works:
(3x^4)(4x^12) = 3 * 4 * x^4 * x^12
= 12 * x^(4+12)
= 12x^16
3. ab^-6 / c^0d^-4:
In this equation, we can simplify it using the exponent rules. Any number raised to the power of zero is equal to 1, and the division of variables with negative exponents is transformed into multiplication of their reciprocals. Let's simplify it step by step:
ab^-6 / c^0d^-4 = ab^-6 * 1 / d^-4
= ab^-6 * d^4
= a * b^-6 * d^4
= a * 1 / b^6 * d^4
= ad^4 / b^6
4. x^3y^0(z^-4):
Any number with an exponent of 0 is equal to 1, so y^0 = 1. Therefore, the equation simplifies as follows:
x^3y^0(z^-4) = x^3 * 1 * z^-4
= x^3 * z^-4
= x^3 / z^4
These are the step-by-step solutions for the given equations. Feel free to ask if anything is unclear or if you have any further questions!