Q. Fully simplify using only positive exponents.30x4y718x8yAnswer:
Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression.We have the coefficients 18 and 30. We need to find the greatest common divisor (GCD) of these two numbers to simplify the fraction.The GCD of 18 and 30 is 6.So, we divide both 18 and 30 by 6 to simplify the fraction.18÷6=330÷6=5Now, the simplified coefficient part is 300.
Simplify x Terms: Simplify the x terms using the laws of exponents.We have x8 in the numerator and x4 in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.x4x8=x8−4=x4Now, the x part is simplified to x4.
Simplify y Terms: Simplify the y terms using the laws of exponents.We have y in the numerator and y7 in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.y/y7=y1−7=y−6Since we want only positive exponents, we can write y−6 as 1/y6.Now, the y part is simplified to 1/y6.
Combine Simplified Parts: Combine the simplified parts to form the final answer.We combine the simplified coefficient (53), the simplified x term (x4), and the simplified y term (y61) to get the final simplified expression.The final answer is (53)x4/y6.
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