To simplify this expression, we can use the exponent rule that states:
a^m × a^n = a^(m + n)
So, applying this rule to 5^13 × 5^-10:
5^13 × 5^-10 = 5^(13 + (-10))
Since 13 + (-10) = 3, we have:
5^13 × 5^-10 = 5^3
Therefore, the simplified expression is 5^3.
Simplify 5^13×5^-10
27 answers
Simplify 4^14/4^-3
To simplify this expression, we can use the exponent rule that states:
a^m / a^n = a^(m - n)
So, applying this rule to 4^14 / 4^-3:
4^14 / 4^-3 = 4^(14 - (-3))
Since 14 - (-3) = 17, we have:
4^14 / 4^-3 = 4^17
Therefore, the simplified expression is 4^17.
a^m / a^n = a^(m - n)
So, applying this rule to 4^14 / 4^-3:
4^14 / 4^-3 = 4^(14 - (-3))
Since 14 - (-3) = 17, we have:
4^14 / 4^-3 = 4^17
Therefore, the simplified expression is 4^17.
Simplify 7^15/7
To simplify the expression 7^15 / 7, we can use the exponent rule that states:
a^m / a^n = a^(m - n)
In this case, we have:
7^15 / 7 = 7^(15 - 1)
Since 15 - 1 = 14, the simplified expression is:
7^15 / 7 = 7^14
a^m / a^n = a^(m - n)
In this case, we have:
7^15 / 7 = 7^(15 - 1)
Since 15 - 1 = 14, the simplified expression is:
7^15 / 7 = 7^14
Simplify (9^-3)^-4
To simplify the expression (9^-3)^-4, we can use the reciprocal of a power rule, which states:
(a^m)^n = a^(m*n)
Using this rule, we have:
(9^-3)^-4 = 9^((-3)*(-4))
Since -3 * -4 = 12, the simplified expression is:
(9^-3)^-4 = 9^12
(a^m)^n = a^(m*n)
Using this rule, we have:
(9^-3)^-4 = 9^((-3)*(-4))
Since -3 * -4 = 12, the simplified expression is:
(9^-3)^-4 = 9^12
Simplify (x^-2)^-4
To simplify the expression (x^-2)^-4, we can use the reciprocal of a power rule, which states:
(a^m)^n = a^(m*n)
Applying this rule, we have:
(x^-2)^-4 = x^((-2)*(-4))
Since -2 * -4 = 8, the simplified expression is:
(x^-2)^-4 = x^8
Therefore, the simplified expression is x^8.
(a^m)^n = a^(m*n)
Applying this rule, we have:
(x^-2)^-4 = x^((-2)*(-4))
Since -2 * -4 = 8, the simplified expression is:
(x^-2)^-4 = x^8
Therefore, the simplified expression is x^8.
Simplify (8^6)^6
To simplify the expression (8^6)^6, we can use the power of a power rule, which states:
(a^m)^n = a^(m*n)
Using this rule, we have:
(8^6)^6 = 8^(6*6)
Since 6 * 6 = 36, the simplified expression is:
(8^6)^6 = 8^36
Therefore, the simplified expression is 8^36.
(a^m)^n = a^(m*n)
Using this rule, we have:
(8^6)^6 = 8^(6*6)
Since 6 * 6 = 36, the simplified expression is:
(8^6)^6 = 8^36
Therefore, the simplified expression is 8^36.
6^-7×6×6^-3
To simplify this expression, we can combine the terms with the same base.
First, let's simplify 6^-7 × 6.
According to the exponent rule that states:
a^m × a^n = a^(m + n)
We have:
6^-7 × 6 = 6^(-7 + 1) = 6^-6
Now, let's simplify 6^-6 × 6^-3.
Using the same exponent rule, we have:
6^-6 × 6^-3 = 6^(-6 + (-3)) = 6^-9
Therefore, the simplified expression is 6^-9.
First, let's simplify 6^-7 × 6.
According to the exponent rule that states:
a^m × a^n = a^(m + n)
We have:
6^-7 × 6 = 6^(-7 + 1) = 6^-6
Now, let's simplify 6^-6 × 6^-3.
Using the same exponent rule, we have:
6^-6 × 6^-3 = 6^(-6 + (-3)) = 6^-9
Therefore, the simplified expression is 6^-9.
Simplify (y^4/y^2)^2×(y^7/y^5)^5
To simplify the expression, we can simplify the terms individually and then combine them.
First, let's simplify (y^4/y^2)^2:
Using the exponent rule that states:
(a / b)^n = a^n / b^n
We have:
(y^4 / y^2)^2 = (y^(4-2))^2 = y^2^2 = y^4
Next, let's simplify (y^7/y^5)^5:
Using the same exponent rule, we have:
(y^7 / y^5)^5 = (y^(7-5))^5 = y^2^5 = y^10
Now, we can multiply the simplified terms together:
(y^4) × (y^10) = y^(4+10) = y^14
Therefore, the simplified expression is y^14.
First, let's simplify (y^4/y^2)^2:
Using the exponent rule that states:
(a / b)^n = a^n / b^n
We have:
(y^4 / y^2)^2 = (y^(4-2))^2 = y^2^2 = y^4
Next, let's simplify (y^7/y^5)^5:
Using the same exponent rule, we have:
(y^7 / y^5)^5 = (y^(7-5))^5 = y^2^5 = y^10
Now, we can multiply the simplified terms together:
(y^4) × (y^10) = y^(4+10) = y^14
Therefore, the simplified expression is y^14.
(X^2)^8×x^3
To simplify this expression, we can use the power of a power rule.
According to the rule (a^m)^n = a^(m * n), we can simplify (X^2)^8 as follows:
(X^2)^8 = X^(2 * 8) = X^16
Now, we can multiply X^16 by X^3:
X^16 * X^3 = X^(16 + 3) = X^19
Therefore, the simplified expression is X^19.
According to the rule (a^m)^n = a^(m * n), we can simplify (X^2)^8 as follows:
(X^2)^8 = X^(2 * 8) = X^16
Now, we can multiply X^16 by X^3:
X^16 * X^3 = X^(16 + 3) = X^19
Therefore, the simplified expression is X^19.
(X^-3×x^5)^9
To simplify this expression, we can apply the power of a product rule.
According to the rule (ab)^n = a^n * b^n,
we can simplify (X^-3 × x^5)^9 as follows:
(X^-3 × x^5)^9 = (X^(-3 * 9)) × (x^(5 * 9))
Simplifying further, we have:
(X^(-27)) × (x^45)
This cannot be simplified any further, so the simplified expression is:
X^(-27) × x^45.
According to the rule (ab)^n = a^n * b^n,
we can simplify (X^-3 × x^5)^9 as follows:
(X^-3 × x^5)^9 = (X^(-3 * 9)) × (x^(5 * 9))
Simplifying further, we have:
(X^(-27)) × (x^45)
This cannot be simplified any further, so the simplified expression is:
X^(-27) × x^45.
What's the answer
Apologies for the confusion. The simplified expression is actually X^(-27) × x^45. However, if you are looking for a numerical answer and have specific values for X and x, I would need those values in order to provide a numerical result.
Simplify please
Apologies for the confusion. To simplify the expression (X^-3 × x^5)^9, we can apply the power of a product rule as mentioned before.
(X^-3 × x^5)^9 = X^(-3*9) × x^(5*9) = X^(-27) × x^45
Therefore, the simplified expression is X^(-27) × x^45.
(X^-3 × x^5)^9 = X^(-3*9) × x^(5*9) = X^(-27) × x^45
Therefore, the simplified expression is X^(-27) × x^45.
Naur that's wrong
I apologize for the incorrect response earlier. Let's simplify the expression correctly:
To simplify (X^-3 × x^5)^9, we can apply the power of a product rule as mentioned before.
(X^-3 × x^5)^9 = X^(-3 * 9) × x^(5 * 9) = X^(-27) × x^45
Since X^-27 represents 1/X^27 (the negative exponent makes the base reciprocal), the expression can be further simplified as follows:
(X^-3 × x^5)^9 = 1/(X^27) × x^45 = x^45/X^27
Therefore, the correct simplified expression is x^45/X^27.
To simplify (X^-3 × x^5)^9, we can apply the power of a product rule as mentioned before.
(X^-3 × x^5)^9 = X^(-3 * 9) × x^(5 * 9) = X^(-27) × x^45
Since X^-27 represents 1/X^27 (the negative exponent makes the base reciprocal), the expression can be further simplified as follows:
(X^-3 × x^5)^9 = 1/(X^27) × x^45 = x^45/X^27
Therefore, the correct simplified expression is x^45/X^27.
(X^-9×x^2)^2/(x^3×x^4)^3
To simplify this expression, we can apply the power of a product rule and simplify the powers separately.
First, let's simplify (X^-9 × x^2)^2:
Using the power of a product rule, we have: (X^-9 × x^2)^2 = X^(-9 * 2) × x^(2 * 2) = X^-18 × x^4
Next, let's simplify (x^3 × x^4)^3:
Using the power of a product rule, we have: (x^3 × x^4)^3 = x^(3*3) × x^(4*3) = x^9 × x^12 = x^(9+12) = x^21
Therefore, the simplified expression is: (X^-9 × x^2)^2/(x^3 × x^4)^3 = (X^-18 × x^4)/x^21 = X^-18 × x^4/x^21 = X^-18 × x^(4-21) = X^-18 × x^-17 = 1/(X^18 × x^17)
First, let's simplify (X^-9 × x^2)^2:
Using the power of a product rule, we have: (X^-9 × x^2)^2 = X^(-9 * 2) × x^(2 * 2) = X^-18 × x^4
Next, let's simplify (x^3 × x^4)^3:
Using the power of a product rule, we have: (x^3 × x^4)^3 = x^(3*3) × x^(4*3) = x^9 × x^12 = x^(9+12) = x^21
Therefore, the simplified expression is: (X^-9 × x^2)^2/(x^3 × x^4)^3 = (X^-18 × x^4)/x^21 = X^-18 × x^4/x^21 = X^-18 × x^(4-21) = X^-18 × x^-17 = 1/(X^18 × x^17)
3 answers