Can you check the following questions,please?
Simplify
30. (-2y)^0/(3x^2)^-3
= 1/(3^-3)(x^-6)
= 1/-27x^-6
= 27x^6
42. (-7x^5/14y^3)^3
= (-1^3)(x^15)/(2^3)(y^9)
= (-1x^15)/8y^9
#30 Your answer is fine, but line 3 has a spurious "-" in -27. Either it was a typo, or you lost it by accident. In any case, 3^-3 = 27, not -27.
Your other syntax is also mangled.
1/((3^-3)(x^-6))
= 1/(1/27 x^-6)
= 27x^6
Your mixing up fractions and negative exponents can cause confusion. I'd have nixed the negative exponents right up front:
1/(3x^2)^-3
= (3x^2)^3
= 27x^6
#42: again correct, but all those factors being cubed confuses me.
(-7x^5/14y^3)^3
= (-x^5/2y^3)^3
= -x^15/8y^9
Thanks for showing how you got rid of the negative exponent on #30. As for #42, that's just how it was on the worksheet. Thanks again.
Let's simplify the given expressions step by step.
30. (-2y)^0 / (3x^2)^-3
To simplify this expression, we need to understand two rules of exponents:
1) Any number raised to the power of zero is always equal to 1.
2) When a negative exponent is applied to a term, it can be moved to the denominator by changing the sign of the exponent.
Using these rules, let's simplify the expression:
(-2y)^0 / (3x^2)^-3
Since (-2y) raised to the power of zero is equal to 1, we can replace (-2y)^0 with 1:
1 / (3x^2)^-3
Now, applying the negative exponent, we move (3x^2)^-3 to the denominator and change the sign of the exponent:
1 / (1 / (3x^2)^3)
Simplifying further, we can raise (3x^2) to the power of 3:
1 / (1 / (27x^6))
To divide by a fraction, we can multiply by its reciprocal:
1 * (27x^6 / 1)
Finally, multiplying 1 by 27x^6 gives us the simplified expression:
27x^6
Therefore, the simplified form of (-2y)^0 / (3x^2)^-3 is 27x^6.
42. (-7x^5 / 14y^3)^3
Using the rule of exponents, when we raise a fraction to a power, we raise both the numerator and denominator to that power:
(-7x^5 / 14y^3)^3
Now, let's simplify the numerator and denominator separately:
Numerator: (-7)^3 * (x^5)^3
The cube of -7 is -343.
The cube of x^5 is x^15.
Denominator: (14)^3 * (y^3)^3
The cube of 14 is 2744.
The cube of y^3 is y^9.
Putting it all together, we have:
(-7x^5 / 14y^3)^3 = -343x^15 / 2744y^9
However, we can simplify this fraction further:
-343 divided by 2744 equals -1/8.
x^15 divided by x^9 equals x^6.
So, the simplified form of (-7x^5 / 14y^3)^3 is:
(-1/8) * x^6 / y^9
Therefore, the simplified form of the expression is -x^6 / 8y^9.