Question

Solve the equation.
-5y + 12(y - 2) = 4
Answer
Simplify.
2x^-5
Answer
Use the commutative and associative properties of real numbers and the properties of exponents to simplify the expression.
(-10y^5x^4)(4x^2y^10)
Answer
Simplify the expression. Write the answer in exponent form.
t^7 ∙ t^4
Answer
Evaluate the expression.
(-9)^2
Answer
Simplify.
(-7y^4)^0
Answer
Solve the equation.
-7 + 12z = 17 + 4z
Answer
Simplify the expression.
(4a^8b^7^-3/a^6b^6^-3)
Answer
simplify the expression (4x^8)^4
Answer
Simplify. Write your answer in exponent form.
(z^2)^8
Answer
Simplify.
(7/8)^-2
Answer
Simplify. Write in exponent form

x^2x^3/x^2
Answered by GPT 3.5
Starting with the equation:
-5y + 12(y - 2) = 4

Simplify the equation by performing the operation inside the parentheses on the left side:
-5y + 12y - 24 = 4

Combine the like terms on the left side of the equation:
7y - 24 = 4

Add 24 to both sides to isolate the variable:
7y = 28

Divide both sides by 7 to solve for y:
y = 4

Therefore, the solution to the equation is y = 4.
Answered by GPT 3.5
To simplify 2x^(-5), we need to rewrite it with a positive exponent.

Recall that x^(-n) is equal to 1/x^n.

So, applying this property to 2x^(-5), we get:

2/x^5

Therefore, the simplified form of 2x^-5 is 2/x^5.
Answered by GPT 3.5
To simplify the expression (-10y^5x^4)(4x^2y^10), we can use the commutative and associative properties of real numbers as well as the properties of exponents.

First, let's rearrange the terms to group the like terms together:

(-10)(4)(x^4)(x^2)(y^5)(y^10)

Next, we can use the associative property to multiply the constants (-10)(4) first:

-40(x^4)(x^2)(y^5)(y^10)

Now, let's simplify the powers of x by adding the exponents when multiplying:

-40(x^(4+2))(y^5)(y^10)

Simplifying further:

-40(x^6)(y^5)(y^10)

Lastly, using the properties of exponents, we can add the exponents of y when multiplying:

-40(x^6)(y^(5+10))

Simplifying the exponent of y:

-40(x^6)(y^15)

Therefore, the simplified expression of (-10y^5x^4)(4x^2y^10) is -40(x^6)(y^15).
Answered by GPT 3.5
To simplify the expression t^7 ∙ t^4, we can use the property of exponents that states when multiplying two powers with the same base, we add their exponents.

Therefore, t^7 ∙ t^4 can be simplified as t^(7 + 4), which gives us t^11.

The simplified expression is t^11.
Answered by GPT 3.5
To evaluate the expression (-9)^2, we need to square the number inside the parentheses.

(-9)^2 = (-9) × (-9) = 81

Therefore, (-9)^2 equals 81.
Answered by GPT 3.5
To simplify the expression (-7y^4)^0, we need to recall the property of exponents that states any number raised to the power of zero is equal to 1.

Therefore, (-7y^4)^0 simplifies to 1.

Therefore, (-7y^4)^0 = 1.
Answered by GPT 3.5
To solve the equation -7 + 12z = 17 + 4z, we want to isolate the variable z on one side of the equation.

First, let's simplify both sides by combining like terms:

-7 + 12z = 17 + 4z

Next, let's move the terms with z to one side and the other constants to the other side:

12z - 4z = 17 + 7

Simplifying:

8z = 24

Finally, to solve for z, we divide both sides of the equation by 8:

(8z)/8 = 24/8

z = 3

Therefore, the solution to the equation -7 + 12z = 17 + 4z is z = 3.
Answered by GPT 3.5
To simplify the expression (4a^8b^7^-3/a^6b^6^-3), we can simplify the exponent terms and apply the division property of exponents.

First, let's simplify the exponents:

a^8 becomes a^(8-6) = a^2

b^7^-3 becomes b^(7*(-3)) = b^(-21)

b^6^-3 becomes b^(6*(-3)) = b^(-18)

Now, let's rewrite the expression with the simplified exponents:

(4a^2b^-21)/(a^6b^-18)

Next, we can simplify the division of exponents by subtracting the exponents in the denominator from the exponents in the numerator:

4a^(2-6)b^(-21--18)

Simplifying further:

4a^(-4)b^(-3)

Finally, using the negative exponent rule, we can rewrite the expression with positive exponents:

4/(a^4b^3)

Therefore, the simplified expression of (4a^8b^7^-3/a^6b^6^-3) is 4/(a^4b^3).
Answered by GPT 3.5
To simplify the expression (4x^8)^4, we need to apply the power of a power rule, which states that when a power is raised to another power, we multiply the exponents.

(4x^8)^4 = 4^4 * (x^8)^4

Simplifying 4^4, we get:

256 * (x^8)^4

Now, applying the power rule, we multiply the exponents of x:

256 * x^(8 * 4)

Simplifying 8 * 4, we have:

256 * x^32

Therefore, the simplified expression (4x^8)^4 is equal to 256x^32.
Answered by GPT 3.5
To simplify the expression (z^2)^8, we apply the power of a power rule. This rule states that when a power is raised to another power, we multiply the exponents.

In this case, we multiply the exponent 2 by the exponent 8:

(z^2)^8 = z^(2 * 8)

Simplifying the exponent 2 * 8, we have:

(z^2)^8 = z^16

Therefore, the simplified expression (z^2)^8 is equal to z^16.
Answered by GPT 3.5
To simplify the expression (7/8)^-2, we can apply the negative exponent rule. This rule states that any expression with a negative exponent can be rewritten by taking the reciprocal of the expression and changing the sign of the exponent to positive.

Therefore, (7/8)^-2 can be rewritten as the reciprocal, 1 / (7/8)^2.

Now, let's simplify (7/8)^2. This involves raising both the numerator and the denominator of (7/8) to the power of 2:

(7/8)^2 = (7^2) / (8^2) = 49/64.

Plugging this value back into the expression, we have:

1 / (49/64).

To divide by a fraction, we can multiply by its reciprocal:

1 * (64/49) = 64/49.

Therefore, the simplified expression (7/8)^-2 is equal to 64/49.
Answered by GPT 3.5
To simplify the expression x^2 * x^3 / x^2, we can use the property of exponents that states when dividing powers with the same base, we subtract their exponents.

In this case, we subtract the exponent of x^2 from the exponent of x^3:

x^2 * x^3 / x^2 = x^(2+3-2) = x^3.

Therefore, the simplified expression is x^3.