Simplify and write x^-8\cdotx^-2 in exponential form with positive exponents only
To simplify and write the expression x^-8 * x^-2 in exponential form with positive exponents only, we can use the properties of exponents.
We know that when multiplying two terms with the same base, we add their exponents. So, applying this property to our expression, we have:
x^-8 * x^-2 = x^(-8 + -2)
Next, we can simplify the exponent by adding -8 and -2, which gives us:
x^(-10)
Since we want to express the exponent in positive form, we can rewrite x^(-10) as 1/x^10.
Therefore, x^-8 * x^-2 = 1/x^10.
Simplify 3^-6×3×3^-5
To simplify the expression 3^-6 × 3 × 3^-5, we can apply the properties of exponents.
First, let's simplify each term with a negative exponent separately:
3^-6 = 1/3^6
3^-5 = 1/3^5
Now, let's substitute these values back into the original expression:
1/3^6 × 3 × 1/3^5
Next, let's multiply the numerators together and the denominators together:
(1 × 3 × 1) / (3^6 × 3^5)
Simplifying further:
3 / (3^(6 + 5))
Adding the exponents:
3 / 3^11
Finally, let's express this back in exponential form with positive exponents only:
1 / 3^11
So, 3^-6 × 3 × 3^-5 simplifies to 1 / 3^11.
Can you write it in exponential form? Also use only positive exponents.... I forgot to ask
Certainly! To write the expression 3^-6 × 3 × 3^-5 in exponential form with positive exponents only, we can use the property that states a^(-n) = 1 / a^n.
So, let's rewrite each term using this property:
3^-6 = 1 / 3^6
3^-5 = 1 / 3^5
Substituting these values back into the original expression:
(1 / 3^6) × 3 × (1 / 3^5)
Next, let's multiply the numerators together and the denominators together:
(1 × 3 × 1) / (3^6 × 3^5)
Simplifying further:
3 / (3^(6 + 5))
Adding the exponents:
3 / 3^11
Finally, let's express this in exponential form with positive exponents:
3^(1 - 11)
Simplifying the exponent:
3^(-10)
So, 3^-6 × 3 × 3^-5 can be written as 3^(-10) in exponential form with positive exponents only.
Simplify and write 1/y×1/y×1/y×1/y×1/y×1/y in exponential form with positive exponents only.
To simplify and write the expression (1/y) × (1/y) × (1/y) × (1/y) × (1/y) × (1/y) in exponential form with positive exponents only, we can combine the factors and use the property that states (a/b)^n = a^n / b^n.
Rewriting the expression as 1/y^6, the original expression can be simplified to y^-6.
In exponential form with positive exponents only, we can write this as 1/y^6 = 1/(y^6).
Simplify and write 1/6^5×1/6^5 in exponential form with positive exponents only.
To simplify and write 1/6^5 × 1/6^5 in exponential form with positive exponents only, we can use the property that states (a/b)^n = a^n / b^n.
Let's rewrite the expression as (1/6^5) × (1/6^5) = (1/6^5)^2.
Applying the property, we can simplify further: (1^2) / (6^5)^2.
Simplifying (1^2) to 1, we have: 1 / (6^5)^2.
Now, we can express this in exponential form with positive exponents only.
Let's write 6^5 as a single term: (6^5)^2 = 6^(5*2) = 6^10.
Therefore, 1/6^5 × 1/6^5 simplifies to 1 / 6^10 in exponential form with positive exponents only.