Simplify (x^5)^0\cdotx^9

Answer 1

(x^5)^0 * x^9

Anything raised to the power of 0 is equal to 1:

1 * x^9

Simplifying further:

x^9

Answer 2

Simplify (z^6\cdotz^7)^5/(z^5\cdotz^2)^3

Answer 3

To simplify this expression, we can first apply the power rule for exponents:

(z^6 * z^7)^5 / (z^5 * z^2)^3

= z^(6*5 + 7*5) / z^(5*3 + 2*3)

= z^55 / z^15

Next, we can use the quotient rule for exponents:

= z^(55-15)

= z^40

Answer 4

Simplify (y^-4\cdoty^-7)^3

Answer 5

To simplify this expression, we can apply the power rule for exponents:

(y^-4 * y^-7)^3

Using the product rule, we can multiply the exponents:

y^(-4*3) * y^(-7*3)

Simplifying further:

y^(-12) * y^(-21)

Using the product rule again, we can add the exponents:

y^(-12 - 21)

Simplifying further:

y^(-33)

Therefore, the simplified expression is y^(-33).

Answer 6

Apply the properties of integer exponents to generate an expression equivalent to 3^7×3^-9 with only positive exponents then solve the expression

The answer will be a simplified fraction with no remaining exponents

Answer 7

To convert the expression 3^7 * 3^-9 with only positive exponents, we can make use of the property of negative exponents: a^(-n) = 1 / a^n.

First, let's rewrite the expression using this property:

3^7 * 3^-9 = 3^7 * (1 / 3^9)

Applying the product rule for exponents, we can combine the terms:

3^7 * (1 / 3^9) = 3^(7 - 9)

Simplifying the exponent:

= 3^(-2)

Using the property of negative exponents again, we can convert this to a positive exponent:

3^(-2) = 1 / 3^2

Evaluating 3^2:

1 / 3^2 = 1 / 9

Therefore, the simplified fraction without remaining exponents is 1/9.

Answer 8

Apply the properties of integer exponents to generate an expression equivalent to 2^2/2^-4 with only positive exponents then solve the expression

Provide it as a whole number

Answer 9

To convert the expression 2^2 / 2^-4 with only positive exponents, we can use the property of negative exponents: a^(-n) = 1 / a^n.

First, let's rewrite the expression using this property:

2^2 / 2^-4 = 2^2 / (1 / 2^4)

Using the property of division with exponents, we subtract the exponents when dividing with the same base:

= 2^2 * 2^4

Applying the product rule for exponents, we can combine the terms:

= 2^(2+4)

Simplifying the exponent:

= 2^6

Since there are no remaining exponents, we can directly evaluate 2^6:

= 64

Therefore, the expression simplifies to the whole number 64.

Answer 10

Apply the properties of integer exponents to generate an expression equivalent to 4^0×5^-2/(-2)^-3 with only positive exponents then solve the expression

It will be simplified with no remaining exponents

Answer 11

To convert the expression 4^0 * 5^-2 / (-2)^-3 with only positive exponents, we can use the property of negative exponents: a^(-n) = 1 / a^n.

First, let's simplify each part of the expression using the properties of exponents:

4^0 * 5^-2 / (-2)^-3

Since any number raised to the power of 0 is equal to 1, we have:

1 * 5^-2 / (-2)^-3

Now, let's convert the negative exponents to positive exponents using the property mentioned earlier:

1 / 5^2 / (1 / (-2)^3)

Applying the property of division with exponents, we can subtract the exponents when dividing with the same base:

= 1 / 5^2 * (-2)^3

Simplifying the exponents:

= 1 / 25 * (-8)

Next, let's simplify the division:

= -8/25

Therefore, the simplified expression with no remaining exponents is -8/25.

Answer 12

Apply the properties of integer exponents to generate an expression equivalent to (14^3×27^-7)^0/3^4 with only positive exponents then solve the expression

It will be a simplified fraction with no remaining exponents

Answer 13

To convert the expression (14^3 * 27^-7)^0 / 3^4 with only positive exponents, we can use the property of negative exponents: a^(-n) = 1 / a^n.

First, let's simplify each part of the expression using the properties of exponents:

(14^3 * 27^-7)^0 / 3^4

Since any number raised to the power of 0 is equal to 1, we have:

1^0 / 3^4

Simplifying further:

1 / 3^4

Now we have the expression 1 / 3^4. We can evaluate this by expanding 3^4:

1 / 3^4 = 1 / (3 * 3 * 3 * 3) = 1 / 81

Therefore, the simplified fraction with no remaining exponents is 1/81.

Answer 14

Apply the properties of integer exponents to generate an expression equivalent to (4^3×7^-2)^-5/7^9×4^-13 with only positive exponents then solve the expression

It will be a simplified fraction with no remaining exponents

Answer 15

To convert the expression (4^3 * 7^-2)^-5 / 7^9 * 4^-13 with only positive exponents, we can use the properties of exponents.

First, let's simplify each part of the expression using the properties of exponents:

(4^3 * 7^-2)^-5 / 7^9 * 4^-13

Using the property of negative exponents, we can rewrite the expression:

(4^3 * 1/7^2)^-5 / 7^9 * 1/4^13

Simplifying the exponents and combining the terms:

(64 * 1/49)^-5 / 7^9 * 1/4^13

Using the property of division with exponents, we can subtract the exponents when dividing with the same base:

= (64 / 49)^-5 / 7^9 * 1/4^13

Now let's simplify the fractions:

= (64 / 49)^-5 / 7^9 * 1/2^26

Using the property of negative exponents, we convert the expression into positive exponents:

= (49 / 64)^5 * 7^-9 * 2^(-26)

Now we have an expression with only positive exponents. Let's simplify further:

= (49^5 / 64^5) * 7^-9 * 2^(-26)

= 49^5 * 64^-5 * 7^-9 * 2^(-26)

Using the property of negative exponents, we can rewrite the expression with positive exponents:

= 49^5 / 64^5 * 1/7^9 * 1/2^26

Now let's simplify the expression:

= (49/64)^5 * 1/(7^9 * 2^26)

= (49/64)^5 / (7^9 * 2^26)

Therefore, the simplified fraction with no remaining exponents is (49/64)^5 / (7^9 * 2^26).