simplify using only positive exponents:
(2t)^-6
can you help me bot
Certainly!
To simplify (2t)^-6 using only positive exponents, we can use the rule for negative exponents:
a^-n = 1 / a^n
In this case, a=2t and n=6:
(2t)^-6 = 1 / (2t)^6
Now we can expand and simplify the denominator using the rule for exponents:
(2t)^6 = 2^6 * t^6 = 64t^6
So we have:
(2t)^-6 = 1 / (2t)^6 = 1 / (64t^6)
And that's the simplified form with only positive exponents!
simplify using only positive exponents:
(w^-2 J^-4)^-3(J^7J^3)
Sure! Here's how we can simplify this expression using only positive exponents:
First, we'll simplify the expression inside the parentheses and combine like terms:
J^7J^3 = J^(7+3) = J^10
Now we can rewrite the expression with the negative exponent as a fraction with a positive exponent:
(w^-2 J^-4)^-3 = (1/w^2J^4)^3 = (1/w^6J^12)
Finally, we'll substitute this into the original expression, and simplify further:
(w^-2 J^-4)^-3(J^7J^3) = (1/w^6J^12) * J^10 = J^(10-12) / w^6 = J^-2 / w^6
So, the simplified expression with only positive exponents is J^-2 / w^6.
simplify using only positive exponents:
a^2b^-7c^4/a^5b^3C^-2
Sure! Here's how we can simplify the expression using only positive exponents:
First, we can simplify the individual factors inside the fraction by applying the rules of exponents:
a^2b^-7c^4 = a^2/c^4b^7
a^5b^3c^-2 = b^3a^5/c^2
Now we can substitute these into the fraction and simplify further:
a^2b^-7c^4/a^5b^3C^-2 = (a^2/c^4b^7) / (b^3a^5/c^2)
We can simplify this further by dividing the coefficients and variables separately:
(a^2/c^4b^7) / (b^3a^5/c^2) = (a^2/c^4 * c^2 / b^7b^3 * 1/a^5)
= (a^2a^-5) / (b^10c^2)
= a^(-3) / (b^10c^2)
So, the simplified expression with only positive exponents is a^(-3) / b^10c^2.
Evaluate the expression for m = 2, t = −3, and z = 0. z−t(mt)z
When m=2, t=-3, and z=0, we can plug in these values to evaluate the expression:
z - t(mt)z
= 0 - (-3) * (2*(-3)*0) * 0
= 0 - (-3) * 0 * 0
= 0
So the value of the expression when m=2, t=-3, and z=0 is 0.
Use scientific notation to rewrite the number: a. 0.0002603 in scientific notation
b. 5.38 × 102 in standard notation
(a) To write 0.0002603 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal. We count the number of places we move the decimal point and use that as the exponent of 10.
0.0002603 = 2.603 x 0.0001
We moved the decimal point four places to the right, so the exponent of 10 is -4. Therefore, 0.0002603 in scientific notation is:
2.603 x 10^-4
(b) To convert 5.38 x 10^2 to standard notation, we just write out the digits and move the decimal point to the right or left depending on the sign of the exponent.
5.38 x 10^2 = 538
We moved the decimal point two places to the right, which is the same as multiplying by 100, so 5.38 x 10^2 in standard notation is:
538