To simplify the expression z^-4 x z^-9, we can use the rule of exponents that states when multiplying powers with the same base, add the exponents.
Using this rule, we add -4 and -9:
z^-4 x z^-9 = z^(-4 + -9)
Simplifying the exponent gives:
z^(-13)
So, z^-4 x z^-9 = z^-13.
z^-4 x z^-9
11 answers
simplify 9^-8 * 9 * 9^-6
To simplify the expression 9^-8 * 9 * 9^-6, we can use the rule of exponents that states when multiplying powers with the same base, add the exponents.
Using this rule, we add -8 and -6:
9^-8 * 9 * 9^-6 = 9^(-8 + 1 + -6)
Simplifying the exponent gives:
9^(-13)
So, 9^-8 * 9 * 9^-6 = 9^(-13).
Using this rule, we add -8 and -6:
9^-8 * 9 * 9^-6 = 9^(-8 + 1 + -6)
Simplifying the exponent gives:
9^(-13)
So, 9^-8 * 9 * 9^-6 = 9^(-13).
simplify (y^5)^9 * y^7
To simplify the expression (y^5)^9 * y^7, we need to apply the rule of exponents that states when raising a power to another power, we multiply the exponents.
Using this rule, we have:
(y^5)^9 * y^7 = y^(5*9) * y^7
Simplifying the exponents inside the parentheses:
(y^5)^9 * y^7 = y^45 * y^7
Now, using the rule of exponents that states when multiplying powers with the same base, add the exponents:
y^45 * y^7 = y^(45+7)
Therefore, the simplified expression is:
(y^5)^9 * y^7 = y^52
Using this rule, we have:
(y^5)^9 * y^7 = y^(5*9) * y^7
Simplifying the exponents inside the parentheses:
(y^5)^9 * y^7 = y^45 * y^7
Now, using the rule of exponents that states when multiplying powers with the same base, add the exponents:
y^45 * y^7 = y^(45+7)
Therefore, the simplified expression is:
(y^5)^9 * y^7 = y^52
fully simplify (x^-2 * x^6)^8
To simplify the expression (x^-2 * x^6)^8, we first need to simplify the exponent of the base inside the parentheses. According to the rule of exponents, when multiplying powers with the same base, you add the exponents.
So, x^-2 * x^6 becomes x^(-2+6) or x^4.
Now the expression becomes (x^4)^8, which means we raise x^4 to the power of 8.
According to the rule of exponents, when raising a power to another power, you multiply the exponents:
(x^4)^8 = x^(4*8) = x^32.
Therefore, the fully simplified expression is x^32.
So, x^-2 * x^6 becomes x^(-2+6) or x^4.
Now the expression becomes (x^4)^8, which means we raise x^4 to the power of 8.
According to the rule of exponents, when raising a power to another power, you multiply the exponents:
(x^4)^8 = x^(4*8) = x^32.
Therefore, the fully simplified expression is x^32.
fully simplify (y^8 * y^8)^5/y^4 * y^3)^2
To fully simplify the expression (y^8 * y^8)^5 / ((y^4 * y^3)^2), we need to simplify each part of the expression separately and then perform the division.
First, let's simplify the numerator (y^8 * y^8)^5:
Using the rule of exponents that states when raising a power to another power, we multiply the exponents:
(y^8 * y^8)^5 = y^(8*5) * y^(8*5) = y^40 * y^40 = y^80.
Next, let's simplify the denominator ((y^4 * y^3)^2):
Using the rule of exponents that states when multiplying powers with the same base, we add the exponents:
(y^4 * y^3)^2 = y^(4+3)^2 = y^7^2 = y^14.
Now, let's perform the division: y^80 / y^14.
Using the rule of exponents that states when dividing powers with the same base, we subtract the exponents:
y^80 / y^14 = y^(80-14) = y^66.
Therefore, the fully simplified expression is y^66.
First, let's simplify the numerator (y^8 * y^8)^5:
Using the rule of exponents that states when raising a power to another power, we multiply the exponents:
(y^8 * y^8)^5 = y^(8*5) * y^(8*5) = y^40 * y^40 = y^80.
Next, let's simplify the denominator ((y^4 * y^3)^2):
Using the rule of exponents that states when multiplying powers with the same base, we add the exponents:
(y^4 * y^3)^2 = y^(4+3)^2 = y^7^2 = y^14.
Now, let's perform the division: y^80 / y^14.
Using the rule of exponents that states when dividing powers with the same base, we subtract the exponents:
y^80 / y^14 = y^(80-14) = y^66.
Therefore, the fully simplified expression is y^66.
fully simplify (x^9)^3 * x^-7
To fully simplify the expression (x^9)^3 * x^-7, we can use the rule of exponents that states when raising a power to another power, we multiply the exponents and when dividing powers with the same base, subtract the exponents.
First, let's simplify the expression (x^9)^3:
(x^9)^3 = x^(9*3) = x^27.
Now, let's simplify the expression x^-7:
Using the rule of exponents that states when a negative exponent is present, we can move it to the denominator:
x^-7 = 1/x^7.
Now, we can rewrite the expression as:
(x^9)^3 * x^-7 = x^27 * (1/x^7).
Applying the rule of exponents for multiplication:
x^27 * (1/x^7) = x^(27-7) = x^20.
Therefore, the fully simplified expression is x^20.
First, let's simplify the expression (x^9)^3:
(x^9)^3 = x^(9*3) = x^27.
Now, let's simplify the expression x^-7:
Using the rule of exponents that states when a negative exponent is present, we can move it to the denominator:
x^-7 = 1/x^7.
Now, we can rewrite the expression as:
(x^9)^3 * x^-7 = x^27 * (1/x^7).
Applying the rule of exponents for multiplication:
x^27 * (1/x^7) = x^(27-7) = x^20.
Therefore, the fully simplified expression is x^20.