Question

Simplify 5^13×5^-10

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

Simplify 4^14/4^-3

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.

Answer 4

Simplify 7^15/7

Answer 5

[AI-generated answer — Bot GPT 3.5]

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

Answer 6

Simplify (9^-3)^-4

Answer 7

[AI-generated answer — Bot GPT 3.5]

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

Answer 8

Simplify (x^-2)^-4

Answer 9

[AI-generated answer — Bot GPT 3.5]

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.

Answer 10

Simplify (8^6)^6

Answer 11

[AI-generated answer — Bot GPT 3.5]

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.

Answer 12

6^-7×6×6^-3

Answer 13

[AI-generated answer — Bot GPT 3.5]

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.

Answer 14

Simplify (y^4/y^2)^2×(y^7/y^5)^5

Answer 15

[AI-generated answer — Bot GPT 3.5]

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.

Answer 16

(X^2)^8×x^3

Answer 17

[AI-generated answer — Bot GPT 3.5]

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.

Answer 18

(X^-3×x^5)^9

Answer 19

[AI-generated answer — Bot GPT 3.5]

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.

Answer 20

What's the answer

Answer 21

[AI-generated answer — Bot GPT 3.5]

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.

Answer 22

Simplify please

Answer 23

[AI-generated answer — Bot GPT 3.5]

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.

Answer 24

Naur that's wrong

Answer 25

[AI-generated answer — Bot GPT 3.5]

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.

Answer 26

(X^-9×x^2)^2/(x^3×x^4)^3

Answer 27

[AI-generated answer — Bot GPT 3.5]

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)